A solid cube of 4-inch edges has been painted with red, green, and yellow colors such that each color appears on a pair of opposite faces. It has been cut into one-inch cubes. The number of small one-inch cubes that have only one face painted with red color is:

Given: A solid cube of 4-inch edges has been painted with red, green, and yellow colors such that each color appears on a pair of opposite faces. It has been cut into one-inch cubes.

The number of small one-inch cubes that have only one face painted with red color can be counted as below:

The cube is of 4-inch cubes we have: n → 4 ÷ 1 = 4

Number of 1 faces painted with red cube = (n - 2)2 × number of edges → (4 - 2)2 × 6 ⇒ 24

Hence, "Option 2" is the correct answer.

Shortcut Trick For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1,

Number of cubes with 0 side painted = (n - 2)³

Number of cubes with 1 side painted =6(n - 2)2

Number of cubes with 2 sides painted= 12(n - 2)

Number of cubes with 3 sides painted= 8(always)